Plotting MOS I-V

Module by: Bill Wilson

Summary: Plotting MOS I-V, and sketching the I-V behavior.

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Now we use two of the equations ((Reference) and (Reference)) that we found in the discussion about MOS Regimes to calculate a set of Vdsat Vdsat and Idsat Idsat values for various value of Vgs Vgs . (Note that Vgs Vgs must be greater than VT VT for the two equations to be valid.) When we get the numbers, we build a little table.

Once we have the numbers, then we sketch a piece of graph paper with the proper scale, and plot the points on it. Once the Idsat Idsat , Vdsat Vdsat points have been determined, it is easy to sketch in the I-V behavior. You just draw a curve from the origin up to any given point, having it "peak out" just at the dot, and then draw a straight line at Idsat Idsat to finish things off. One such curve is shown in Figure 3. And then finally in Figure 4 they are all sketched in. Your curves probably wont be exactly right but they will be good enough for a lot of applications.

Figure 2: Plotting Idsat Idsat and Vdsat Vdsat .

Figure 3: Sketching in one of the I-V curves.

Figure 4: The complete set of curves.

There is a particularly easy way to measure by kk and VT VT for a MOSFET. Let's first introduce the schematic symbol for the MOSFET, it looks like Figure 5. Let's take a MOSFET and hook it up as shown in Figure 6.

Figure 5: Schematic symbol for a MOSFET

Figure 6: Circuit for finding VT VT and kk

Since the gate of this transistor is connected to the drain, there is no doubt that V gs − V ds V gs V ds is less than VT VT . In fact, since V gs = V ds V gs V ds , their difference, is zero. Thus, for any value of Vds Vds , this transistor is operating in its saturated condition. Since V gs = V ds V gs V ds , we can rewrite a previous equation derived equation from the section on MOS transistor as

Now let's take the square root of both sides:

So if we make a plot of I d I d as a function of Vds Vds , we should get a straight line, with a slope of k2 k 2 and an x-intercept of VT VT .

Figure 7: Obtaining VT VT and kk

Because of the expected non-ideality, the curve does not go all the way to VT VT , but deviates a bit near the bottom. A simple linear extrapolation of the straight part of the plot however, yields an unambiguous value for the threshold voltage VT VT .

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This work is licensed by Bill Wilson under a Creative Commons Attribution License (CC-BY 1.0), and is an Open Educational Resource.

Last edited by Raymond Wagner on Aug 14, 2007 11:51 am GMT-5.